A moment map for the G-action on (M, ω) is a map such that
for all ξ in . Here is the function from M to R defined by . The moment map is uniquely defined up to an additive constant of integration.
A moment map is often also required to be G-equivariant, where G acts on via the coadjoint action. If the group is compact or semisimple, then the constant of integration can always be chosen to make the moment map coadjoint equivariant; however in general the coadjoint action must be modified to make the map equivariant (this is the case for example for the Euclidean group).
Read more about Moment Map: Hamiltonian Group Actions, Examples, Symplectic Quotients
Famous quotes containing the words moment and/or map:
“Art knows no happier moment than the opportunity to show the symmetry of an extreme, during that moment of spheric harmony when the dissonance dissolves for the blink of an eye, dissolves into a blissful harmony, when the most extreme opposites, coming together from the greatest alienation, fleetingly touch with lips of the word and of love.”
—Stefan Zweig (18811942)
“A map of the world that does not include Utopia is not worth even glancing at, for it leaves out the one country at which Humanity is always landing.”
—Oscar Wilde (1854–1900)